Subgroups — C₇₁×#19202 #31840074

Order 18176.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3208	C₂	1	1	yes	maximal, characteristic
3	C₂×#492×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1686	C₂	1	4	yes	maximal, complemented
6	C₇₁×#1666	C₂	1	4	yes	maximal, complemented
7	C₇₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#1545	C₂	1	1	yes	maximal, characteristic
10	C₂²×SD₁₆×C₇₁	—	2	1	no	—
11	C₂²×SD₁₆×C₇₁	—	2	1	no	—
12	#533×C₇₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×#127×C₇₁	C₂²	1	1	yes	characteristic
15	#498×C₇₁	—	2	1	no	—
16	#492×C₇₁	—	2	1	no	—
17	#492×C₇₁	—	2	1	no	—
18	#492×C₇₁	—	2	1	no	—
19	#492×C₇₁	C₂²	1	2	yes	—
20	#492×C₇₁	C₂²	1	2	yes	—
21	#487×C₇₁	—	2	1	no	—
22	#486×C₇₁	—	2	1	no	—
23	#483×C₇₁	—	2	2	no	—
24	#475×C₇₁	C₂²	1	4	yes	complemented
25	#460×C₇₁	C₂²	1	4	yes	—
26	#450×C₇₁	—	2	2	no	—
27	#446×C₇₁	—	2	1	no	—
28	#446×C₇₁	C₂²	1	2	yes	complemented
29	C₈×Q₈×C₇₁	—	2	1	no	—
30	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
31	#431×C₇₁	C₂²	1	1	yes	characteristic
32	#431×C₇₁	C₂²	1	1	yes	characteristic
33	#424×C₇₁	—	2	1	no	—
34	#423×C₇₁	C₂²	1	1	yes	characteristic
35	#405×C₇₁	—	2	1	no	—
36	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
37	#335×C₇₁	C₂²	1	2	yes	complemented
38	#334×C₇₁	C₂²	1	2	yes	complemented
39	#332×C₇₁	C₂²	1	4	yes	complemented
40	#331×C₇₁	C₂²	1	4	yes	—
41	C₂²×Q₈×C₇₁	—	2	1	no	—
42	C₂²×D₄×C₇₁	—	2	1	no	—
43	C₂²×D₄×C₇₁	—	2	1	no	—
44	C₂²×D₄×C₇₁	—	2	1	no	—
45	C₂×SD₁₆×C₇₁	—	2	4	no	—
46	C₂×SD₁₆×C₇₁	—	2	2	no	—
47	C₂×SD₁₆×C₇₁	—	2	2	no	—
48	C₂×SD₁₆×C₇₁	—	2	2	no	—
49	C₂×SD₁₆×C₇₁	—	2	2	no	—
50	C₂×SD₁₆×C₇₁	—	4	4	no	—
51	C₂×SD₁₆×C₇₁	—	4	4	no	—
52	C₂×M₁₆×C₇₁	—	2	1	no	—
53	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₇₁	—	2	1	no	—
56	C₄⋊Q₈×C₇₁	—	2	1	no	—
57	C₄⋊Q₈×C₇₁	—	2	1	no	—
58	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
59	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
61	#127×C₇₁	—	2	1	no	—
62	#127×C₇₁	—	2	1	no	—
63	#127×C₇₁	—	2	1	no	—
64	#127×C₇₁	C₂³	1	2	yes	—
65	#125×C₇₁	—	2	1	no	—
66	C₂²⋊Q₈×C₇₁	—	2	1	no	—
67	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
68	C₄×Q₈×C₇₁	—	2	1	no	—
69	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
70	#117×C₇₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
73	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
74	#106×C₇₁	—	2	4	no	—
75	C₄⋊C₈×C₇₁	—	2	2	no	—
76	C₄⋊C₈×C₇₁	—	2	2	no	—
77	C₄⋊C₈×C₇₁	—	2	1	no	—
78	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
79	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
81	#103×C₇₁	—	2	4	no	—
82	#102×C₇₁	—	2	4	no	—
83	C₂²⋊C₈×C₇₁	—	2	1	no	—
84	C₂²⋊C₈×C₇₁	—	2	1	no	—
85	#97×C₇₁	—	2	2	no	—
86	C₄×C₈×C₇₁	—	2	2	no	—
87	C₄×C₈×C₇₁	—	2	1	no	—
88	C₄×C₈×C₇₁	—	2	1	no	—
89	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
90	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
91	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
93	C₂⁴×C₇₁	—	4	1	no	—
94	C₂×Q₈×C₇₁	—	2	1	no	—
95	C₂×Q₈×C₇₁	—	2	2	no	—
96	C₂×Q₈×C₇₁	—	4	1	no	—
97	C₂×Q₈×C₇₁	—	4	2	no	—
98	C₂×Q₈×C₇₁	—	4	2	no	—
99	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
100	C₂×D₄×C₇₁	—	2	2	no	—
101	C₂×D₄×C₇₁	—	2	2	no	—
102	C₂×D₄×C₇₁	—	2	2	no	—
103	C₂×D₄×C₇₁	—	4	1	no	—
104	C₂×D₄×C₇₁	—	4	1	no	—
105	C₂×D₄×C₇₁	—	4	1	no	—
106	C₂×D₄×C₇₁	—	4	2	no	—
107	C₂×D₄×C₇₁	—	4	2	no	—
108	C₂×D₄×C₇₁	—	8	2	no	—
109	C₂×D₄×C₇₁	—	8	2	no	—
110	C₂²×C₄×C₇₁	—	4	1	no	—
111	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
114	SD₁₆×C₇₁	—	4	4	no	—
115	SD₁₆×C₇₁	—	4	4	no	—
116	SD₁₆×C₇₁	—	4	4	no	—
117	SD₁₆×C₇₁	—	4	4	no	—
118	SD₁₆×C₇₁	—	8	4	no	—
119	M₁₆×C₇₁	—	4	2	no	—
120	C₂×C₈×C₇₁	—	2	2	no	—
121	C₂×C₈×C₇₁	—	2	2	no	—
122	C₂×C₈×C₇₁	—	2	2	no	—
123	C₂×C₈×C₇₁	—	2	2	no	—
124	C₂×C₈×C₇₁	SD₁₆	1	4	yes	complemented
125	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₇₁	—	2	1	no	—
130	C₄⋊C₄×C₇₁	—	2	1	no	—
131	C₄⋊C₄×C₇₁	—	2	1	no	—
132	C₄⋊C₄×C₇₁	—	2	2	no	—
133	C₄⋊C₄×C₇₁	—	2	2	no	—
134	C₄⋊C₄×C₇₁	—	2	2	no	—
135	C₄⋊C₄×C₇₁	—	2	2	no	—
136	C₄⋊C₄×C₇₁	—	4	1	no	—
137	C₄⋊C₄×C₇₁	—	4	1	no	—
138	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₇₁	—	2	2	no	—
140	C₄²×C₇₁	—	2	2	no	—
141	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₇₁	#41	1	1	yes	characteristic
144	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
145	C₂³×C₇₁	—	4	2	no	—
146	C₂³×C₇₁	—	8	2	no	—
147	C₂³×C₇₁	—	8	2	no	—
148	C₂³×C₇₁	—	8	2	no	—
149	C₂³×C₇₁	#121	1	1	yes	characteristic
150	Q₈×C₇₁	—	2	4	no	—
151	Q₈×C₇₁	—	4	2	no	—
152	Q₈×C₇₁	—	4	2	no	—
153	Q₈×C₇₁	—	4	2	no	—
154	Q₈×C₇₁	—	8	2	no	—
155	D₄×C₇₁	—	4	2	no	—
156	D₄×C₇₁	—	4	2	no	—
157	D₄×C₇₁	—	4	4	no	—
158	D₄×C₇₁	—	8	2	no	—
159	D₄×C₇₁	—	8	2	no	—
160	D₄×C₇₁	—	8	2	no	—
161	D₄×C₇₁	—	8	2	no	—
162	C₂×C₄×C₇₁	—	2	2	no	—
163	C₂×C₄×C₇₁	—	2	2	no	—
164	C₂×C₄×C₇₁	—	2	2	no	—
165	C₂×C₄×C₇₁	—	2	2	no	—
166	C₂×C₄×C₇₁	—	4	2	no	—
167	C₂×C₄×C₇₁	—	8	2	no	—
168	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₇₁	C₂×SD₁₆	1	2	yes	—
172	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
176	C₈×C₇₁	—	2	1	no	—
177	C₈×C₇₁	—	2	1	no	—
178	C₈×C₇₁	—	4	2	no	—
179	C₈×C₇₁	—	4	2	no	—
180	C₈×C₇₁	—	4	2	no	—
181	C₈×C₇₁	C₂×SD₁₆	1	2	yes	—
182	C₈×C₇₁	C₂×SD₁₆	1	2	yes	—
183	C₂²×C₇₁	—	2	1	no	—
184	C₂²×C₇₁	—	2	1	no	—
185	C₂²×C₇₁	—	8	2	no	—
186	C₂²×C₇₁	—	8	2	no	—
187	C₂²×C₇₁	—	8	2	no	—
188	C₂²×C₇₁	—	16	4	no	—
189	C₂²×C₇₁	#460	1	2	yes	—
190	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
191	C₄×C₇₁	—	2	1	no	—
192	C₄×C₇₁	—	2	1	no	—
193	C₄×C₇₁	—	4	2	no	—
194	C₄×C₇₁	—	4	2	no	—
195	C₄×C₇₁	—	8	2	no	—
196	C₄×C₇₁	#460	1	2	yes	—
197	C₄×C₇₁	#471	1	2	yes	—
198	C₄×C₇₁	C₂²×SD₁₆	1	1	yes	characteristic
199	C₄×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₄×C₇₁	#577	1	2	yes	—
201	#19202	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂×C₇₁	—	2	2	no	—
203	C₂×C₇₁	—	16	2	no	—
204	C₂×C₇₁	C₂×#460	1	1	yes	characteristic
205	C₂×C₇₁	#3057	1	1	yes	characteristic
206	C₂×C₇₁	C₂×#471	1	1	yes	characteristic
207	#3229	C₂×C₇₁	1	1	yes	characteristic, complemented
208	#3208	C₂×C₇₁	1	1	yes	characteristic
209	C₂×#492	C₂×C₇₁	1	1	yes	characteristic
210	#2960	C₂×C₇₁	1	1	yes	characteristic, complemented
211	#1686	C₂×C₇₁	1	4	yes	complemented
212	#1666	C₂×C₇₁	1	4	yes	complemented
213	#1564	C₂×C₇₁	1	1	yes	characteristic, complemented
214	#1546	C₂×C₇₁	1	1	yes	characteristic, complemented
215	#1545	C₂×C₇₁	1	1	yes	characteristic
216	C₇₁	#19202	1	1	yes	characteristic, direct product factor, Sylow
217	C₂²×SD₁₆	—	2	1	no	—
218	C₂²×SD₁₆	—	2	1	no	—
219	#533	C₂²×C₇₁	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
221	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
222	#498	—	2	1	no	—
223	#492	—	2	1	no	—
224	#492	—	2	1	no	—
225	#492	—	2	1	no	—
226	#492	C₂²×C₇₁	1	2	yes	—
227	#492	C₂²×C₇₁	1	2	yes	—
228	#487	—	2	1	no	—
229	#486	—	2	1	no	—
230	#483	—	2	2	no	—
231	#475	C₂²×C₇₁	1	4	yes	complemented
232	#460	C₂²×C₇₁	1	4	yes	—
233	#450	—	2	2	no	—
234	#446	—	2	1	no	—
235	#446	C₂²×C₇₁	1	2	yes	complemented
236	C₈×Q₈	—	2	1	no	—
237	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
238	#431	C₂²×C₇₁	1	1	yes	characteristic
239	#431	C₂²×C₇₁	1	1	yes	characteristic
240	#424	—	2	1	no	—
241	#423	C₂²×C₇₁	1	1	yes	characteristic
242	#405	—	2	1	no	—
243	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
244	#335	C₂²×C₇₁	1	2	yes	complemented
245	#334	C₂²×C₇₁	1	2	yes	complemented
246	#332	C₂²×C₇₁	1	4	yes	complemented
247	#331	C₂²×C₇₁	1	4	yes	—
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂×SD₁₆	—	2	4	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	—	2	2	no	—
257	C₂×SD₁₆	—	4	4	no	—
258	C₂×SD₁₆	—	4	4	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂²×C₈	D₄×C₇₁	1	1	yes	characteristic
261	C₂²×C₈	D₄×C₇₁	1	1	yes	characteristic
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
266	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
267	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
268	#127	—	2	1	no	—
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	C₂³×C₇₁	1	2	yes	—
272	#125	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
277	#117	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
281	#106	—	2	4	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
286	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
287	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
288	#103	—	2	4	no	—
289	#102	—	2	4	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	#97	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	D₄×C₇₁	1	1	yes	characteristic
297	C₄×C₈	D₄×C₇₁	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
299	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
300	C₂⁴	—	4	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	8	2	no	—
316	C₂×D₄	—	8	2	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
320	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
321	SD₁₆	—	4	4	no	—
322	SD₁₆	—	4	4	no	—
323	SD₁₆	—	4	4	no	—
324	SD₁₆	—	4	4	no	—
325	SD₁₆	—	8	4	no	—
326	M₁₆	—	4	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	SD₁₆×C₇₁	1	4	yes	complemented
332	C₂×C₈	C₂×D₄×C₇₁	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₇₁	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₇₁	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₇₁	1	1	yes	characteristic
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
350	C₄²	#41×C₇₁	1	1	yes	characteristic
351	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
352	C₂³	—	4	2	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	—	8	2	no	—
356	C₂³	#121×C₇₁	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	8	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	4	no	—
365	D₄	—	8	2	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
376	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
377	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
378	C₂×C₄	C₂×SD₁₆×C₇₁	1	2	yes	—
379	C₂×C₄	AGL(1,ℤ/8)×C₇₁	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	C₂×SD₁₆×C₇₁	1	2	yes	—
389	C₈	C₂×SD₁₆×C₇₁	1	2	yes	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	16	4	no	—
396	C₂²	#460×C₇₁	1	2	yes	—
397	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	2	no	—
403	C₄	#460×C₇₁	1	2	yes	—
404	C₄	#471×C₇₁	1	2	yes	—
405	C₄	C₂²×SD₁₆×C₇₁	1	1	yes	characteristic
406	C₄	C₂×AGL(1,ℤ/8)×C₇₁	1	1	yes	characteristic
407	C₄	#577×C₇₁	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	16	2	no	—
410	C₂	C₂×#460×C₇₁	1	1	yes	characteristic
411	C₂	C₇₁×#3057	1	1	yes	characteristic
412	C₂	C₂×#471×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₁
prime radical	C₂×#127×C₇₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇₁×#3229	C₂	semidirect
4. C₇₁×#2960	C₂	semidirect
5. C₇₁×#1686	C₂	semidirect
6. C₇₁×#1666	C₂	semidirect
7. C₇₁×#1564	C₂	semidirect
8. C₇₁×#1546	C₂	semidirect
24. #475×C₇₁	C₂²	semidirect
28. #446×C₇₁	C₂²	semidirect
30. C₈×Q₈×C₇₁	C₂²	semidirect
37. #335×C₇₁	C₂²	semidirect
38. #334×C₇₁	C₂²	semidirect
39. #332×C₇₁	C₂²	semidirect
124. C₂×C₈×C₇₁	SD₁₆	semidirect
201. #19202	C₇₁	direct (N × H)
207. #3229	C₂×C₇₁	semidirect
210. #2960	C₂×C₇₁	semidirect
211. #1686	C₂×C₇₁	semidirect
212. #1666	C₂×C₇₁	semidirect
213. #1564	C₂×C₇₁	semidirect
214. #1546	C₂×C₇₁	semidirect
216. C₇₁	#19202	direct (N × H)
231. #475	C₂²×C₇₁	semidirect
235. #446	C₂²×C₇₁	semidirect
237. C₈×Q₈	C₂²×C₇₁	semidirect
244. #335	C₂²×C₇₁	semidirect
245. #334	C₂²×C₇₁	semidirect
246. #332	C₂²×C₇₁	semidirect
331. C₂×C₈	SD₁₆×C₇₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇₁×#3229	2
C₇₁×#3208	2
C₂×#492×C₇₁	2
C₇₁×#2960	2
C₇₁×#1686	2
C₇₁×#1666	2
C₇₁×#1564	2
C₇₁×#1546	2
C₇₁×#1545	2
#19202	71

Subgroups — C71×#19202 #31840074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19202 #31840074